A traditional assumption of many translators is that in general the best available avenue back to the “original text” of the Old Testament is through the Masoretic Text (MT). This text is preserved in the great medieval codices such as Leningrad Codex (c. A.D. 1008) used as the basis of Biblia Hebraica Stuttgartensia and the Aleppo Codex (c. A.D. 952) the basis of the “Hebrew University Bible Project.”
It is true that Aleppo Codex was once considered to the most accurate ‘complete Masoretic Text’. However since the riots against Jews in Aleppo in December 1947, the community's ancient synagogue was burned and the Codex was damaged, so that ‘no more than 294 of the original 487 pages survived’. In particular, only the last few pages of the Torah are extant. This makes it pretty much impossible to recreate for the Torah! Therefore now the Leningrad Codex is probably considered the most accurate ‘complete’ copy of the Masoretic Text, and especially for the Torah. Of course there are older and sometimes considered more accurate fragments before these two versions, such as portions of the Dead See Scrolls but these are the oldest MT that were 'once complete'.
So although the lost pages of the Aleppo Codex can’t be restored, as they are lost, there are attempts at restoration of the Hebrew Bible that reproduces the text of the Aleppo Codex. This was begun in 1956 by Moshe Goshen-Gottstein, as the Hebrew University Bible Project. So far, the books of Isaiah, Jeremiah and Ezekiel have been published. Of course where there is no Aleppo Codex, such as in the Torah section, the Leningrad Codex would probably be the first choice with possible corrections from other fragments.
Common sense would dictate that an older text is more accurate especially when it is saying something reasonable, and a later translation is saying something with obvious error. Another strong indication that the MT could be corrupt at a particular point is if the LXX has a very reasonable meaning which through reverse translation explains both the MT and LXX.
For a list of possible sources see here: Hebrew Bible Manuscripts.
Note: I am posting this answer, not as an expert that can answer follow up questions. I have many questions about this subject myself, which I have not got around to asking or researching. Among Christian translations I know there are some competing theories about which texts to use as the 'most reliable' but I really do not know what they are are how close they are to each other. Some, I believe, take consensus approaches and others have decided favor for certain texts.